Irodov Problem 1.172

Let v be ball 1's initial velocity and let the velocities of balls 1 and 2 after the collision be v1 and v1. Since there are no external forces on the system, the momentum must be conserved. So we have,



The kinetic energy after collision decreases by a fraction we have,















Since v1 > v2 is not possible (for this ball 1 would have to pass through ball 2 and move ahead) we choose . This also means that v1 will always be positive, in other words it will not change its direction.